Final answer:
The sacrament specifically focused on nurturing relationships within the Church community is Confirmation. This pledge taken in young adulthood commits the individual to be an active and contributing member of the Church, serving and building connections with other believers.
Step-by-step explanation:
The sacrament recognized as one that contributes to the construction of the Church through the establishment and nurturing of relationships with others is Confirmation. Confirmation is the pledge taken in young adulthood to be a faithful member of the Church. It is a moment when the faithful commit to maintaining and developing their Christian relationships and serving the community of believers, thus significantly contributing to the life and growth of the Church.
While the sacrament of Baptism is indeed important as it marks the entry into the Christian faith by purging the original sin, and the Eucharist is central to Christian practice as it commemorates Christ's sacrifice, these do not directly emphasize the nurturing of relationships within the Church community to the same extent as Confirmation does. The sacrament of Reconciliation, on the other hand, primarily deals with confessing one's sins to God and receiving forgiveness, which is more personal than communal.